The most common and most likely answer to this crossword clue is the 6 letter word HERESY
I've seen this crossword clue in Financial Times
H
E
R
E
S
Y
More clues leading to the result HERESY
- Unorthodox practice in this place is unknown
- Unorthodox belief present with Syria’s leaders
- This is the ultimate in blasphemy?
- Let me introduce Yankee's contrary belief
- Present extremely silly and contrary opinion
- I give you a variable sort of free-thinking
- Present state excludes a non-orthodox view
- I’m showing you yellow, primarily, for dissent
- What Peter Cameron was convicted of, at this place on outskirts of Sydney
- Present leaders of synod display non-conformist belief
Buddy explains!

The straight part
We know that "sort of free-thinking" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sort of free-thinking = heresy.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does HERESY mean?
HERESY noun- A doctrine held by a member of a religion at variance with established religious beliefs, especially dissension from Roman Catholic dogma.
- A controversial or unorthodox opinion held by a member of a group, as in politics, philosophy or science.